Machine and methods for making rolled dielectric elastomer transducers

ABSTRACT

A method for making a rolled dielectric elastomer transducer includes rolling a dielectric film laminate into a solid dielectric elastomer transducer roll. An apparatus includes a drive mechanism for receiving a carrier plate with a dielectric film laminate located on a top surface thereof. The drive mechanism is configured to drive the carrier plate in a first direction. A scrub roller is configured to counter-rotate in a second direction relative to the first direction and frictionally engage the dielectric film to roll the dielectric film laminate into a solid dielectric elastomer transducer roll. The apparatus may also include a fixed jaw and a movable jaw movable relative to the fixed jaw to define a longitudinal aperture for receiving a solid dielectric elastomer transducer roll therein. A cutter is configured to segment the solid dielectric elastomer transducer roll into at least two or more individual solid dielectric elastomer transducer rolls.

RELATED APPLICATIONS

This application claims the benefit, under 35 USC §119(e), of U.S. Provisional Application Nos. 61/683,860 filed Aug. 16, 2012 entitled “ROLL ACTUATORS IN AXIAL TENSION, MODEL AND DATA”; 61/717,810 filed Oct. 24, 2012 entitled “DIELECTRIC ELASTOMER TRANSDUCER WITH QUICK-CONNECT TERMINALS”; 61/719,999 filed Oct. 30, 2012 entitled “MACHINE AND METHODS FOR MAKING ROLLED DIELECTRIC ELASTOMER TRANSDUCERS”; 61/734,609 filed Dec. 7, 2012 entitled “RESONANT FREQUENCIES”; 61/734,616 filed Dec. 7, 2012 entitled “ROLL ACTUATORS”; and 61/734,622 filed Dec. 7, 2012 entitled “SKIN CONTACT WITH DIELECTRIC ELASTOMER ACTUATORS—SYSTEMS FOR SAFETY”; the entirety of each of which is incorporated herein by reference.

FIELD OF THE INVENTION

The present invention is directed in general to electroactive polymers and more specifically to a rolled dielectric elastomer transducer and manufacturing processes and apparatus for making rolled dielectric elastomer transducers.

BACKGROUND OF THE INVENTION

A tremendous variety of devices used today rely on actuators of one sort or another to convert electrical energy to mechanical energy. Conversely, many power generation applications operate by converting mechanical action into electrical energy. Employed to harvest mechanical energy in this fashion, the same type of device may be referred to as a generator. Likewise, when the structure is employed to convert physical stimulus such as vibration or pressure into an electrical signal for measurement purposes, it may be characterized as a sensor. Yet, the term “transducer” may be used to generically refer to any of the devices.

A number of design considerations favor the selection and use of advanced dielectric elastomer materials, also referred to as “electroactive polymers”, for the fabrication of transducers. These considerations include potential force, power density, power conversion/consumption, size, weight, cost, response time, duty cycle, service requirements, environmental impact, etc. As such, in many applications, electroactive polymer technology offers an ideal replacement for piezoelectric, shape-memory alloy and electromagnetic devices such as motors and solenoids.

An electroactive polymer transducer comprises two electrodes having deformable characteristics and separated by a thin elastomeric dielectric material. When a voltage difference is applied to the electrodes, the oppositely charged electrodes attract each other thereby compressing the polymer dielectric layer therebetween. As the electrodes are pulled closer together, the dielectric polymer film becomes thinner (the Z-axis component contracts) as it expands in the planar directions (along the X- and Y-axes), i.e., the displacement of the film is in-plane. The electroactive polymer film may also be configured to produce movement in a direction orthogonal to the film structure (along the Z-axis), i.e., the displacement of the film is out-of-plane. For example, U.S. Pat. No. 7,567,681 discloses electroactive polymer film constructs which provide such out-of-plane displacement—also referred to as surface deformation or as thickness mode deflection.

The material and physical properties of the electroactive polymer film may be varied and controlled to customize the deformation undergone by the transducer. More specifically, factors such as the relative elasticity between the polymer film and the electrode material, the relative thickness between the polymer film and electrode material and/or the varying thickness of the polymer film and/or electrode material, the physical pattern of the polymer film and/or electrode material (to provide localized active and inactive areas), the tension or pre-strain placed on the electroactive polymer film as a whole, and the amount of voltage applied to or capacitance induced upon the film may be controlled and varied to customize the features of the film when in an active mode.

Numerous applications exist that benefit from the advantages provided by such electroactive polymer films whether using the film alone or using it in an electroactive polymer actuator. One of the many applications involves the use of electroactive polymer transducers as actuators to produce haptic, tactile, vibrational feedback (the communication of information to a user through forces applied to the user's body), and the like, in user interface devices. There are many known user interface devices which employ such feedback, typically in response to a force initiated by the user. Examples of user interface devices that may employ such feedback include keyboards, keypads, game controller, remote control, touch screens, computer mice, trackballs, stylus sticks, joysticks, etc. The user interface surface can comprise any surface that a user manipulates, engages, and/or observes regarding feedback or information from the device. Examples of such interface surfaces include, but are not limited to, a key (e.g., keys on a keyboard), a game pad or buttons, a display screen, etc.

The feedback provided by these types of interface devices is in the form of physical sensations, such as vibrations, pulses, spring forces, etc., which a user senses either directly (e.g., via touching of the screen), indirectly (e.g., via a vibrational effect such a when a cell phone vibrates in a purse or bag) or otherwise sensed (e.g., via an action of a moving body that creates a pressure disturbance sensed by the user). The proliferation of consumer electronic media devices such as smart phones, personal media players, portable computing devices, portable gaming systems, electronic readers, etc., can create a situation where a sub-segment of customers would benefit or desire an improved haptic effect in the electronic media device. However, increasing feedback capabilities in every model of an electronic media device may not be justified due to increased cost or increased profile of the device. Moreover, customers of certain electronic media devices may desire to temporarily improve the haptic capabilities of the electronic media device for certain activities.

Use of electroactive polymer materials in consumer electronic media devices as well as the numerous other commercial and consumer applications highlights the need to increase production volume while maintaining precision and consistency of the films.

Conventional rolled dielectric elastomer transducer based cylindrical actuators are desirable because a cylindrical shape is functional and familiar. It matches many mechanical components, such as, for example, solenoids, air cylinders, shock absorbers, etc. so mounting hardware is readily available, for example, the clevis, the ball joint, and the threaded rod. Engineers' familiarity with cylindrical actuators simplifies efforts to integrate them into new designs. Nevertheless, hollow, rolled dielectric elastomer tubes and tubes with an internal spring, called “spring rolls” have some drawbacks. Empty space inside the tube is wasted, making the transducer larger than strictly necessary. Also, accumulated tension from winding the outer layers of the tube tends to buckle and collapse the tube. In a tubular roll made with a highly prestrained acrylic dielectric, this has been found to impose a practical limit of only a few turns per transducer.

The present disclosure provides various improvements over conventional hollow rolled dielectric elastomer transducers and manufacturing processes for making transducers. The present invention overcomes these drawbacks by winding dielectric elastomer films into a solid roll. Among the advantages of a solid roll are that it does not waste space, and it does not collapse as turns are added. A rolling machine also is disclosed, along with a manufacturing process, materials, and fixtures for manufacturing dielectric elastomer actuator rolls with the machine, as described herein in the detailed description of the invention section of the present disclosure.

SUMMARY OF THE INVENTION

In one embodiment, a method comprises providing a dielectric film laminate and rolling the dielectric film laminate into a solid dielectric elastomer transducer roll.

In another embodiment, an apparatus comprises a drive mechanism for receiving a carrier plate with a dielectric film laminate located on a top surface thereof. The drive mechanism is configured to drive the carrier plate in a first direction. A scrub roller is configured to counter-rotate in a second direction relative to the first direction and frictionally engage the dielectric film to roll the dielectric film laminate into a solid dielectric elastomer transducer roll.

In yet another embodiment, the apparatus further comprises a fixed jaw and a movable jaw movable relative to the fixed jaw to define a longitudinal aperture for receiving a solid dielectric elastomer transducer roll therein. A cutter is configured to segment the solid dielectric elastomer transducer roll into at least two or more individual solid dielectric elastomer transducer rolls.

These and other features and advantages of the invention will become apparent to those persons skilled in the art upon reading the details of the invention as more fully described below. In addition, variations of the processes and devices described herein include combinations of the embodiments or of aspects of the embodiments where possible are within the scope of this disclosure even if those combinations are not explicitly shown or discussed.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is best understood from the following detailed description when read in conjunction with the accompanying drawings. To facilitate understanding, the same reference numerals have been used (where practical) to designate similar elements are common to the drawings. Included in the drawings are the following:

FIG. 1 illustrates a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention;

FIG. 2 illustrates tension σ_(p) that accumulates when removing film from a liner while winding a hollow rolled dielectric elastomer transducer;

FIG. 3 illustrates radial stress ΔP developed in the hollow dielectric elastomer transducer rolls shown in FIG. 2 caused by the tension σ_(p);

FIG. 4 is a graphical illustration depicting the accumulation of radial stress ΔP in the hollow dielectric elastomer transducer rolls shown in FIG. 2 as additional wraps are added to the hollow rolled dielectric elastomer transducer;

FIG. 5 illustrates inner windings of a hollow dielectric elastomer transducer rolls that have collapsed under the accumulated radial stress P imposed by tension σ_(p) in the outer windings;

FIG. 6 illustrates a cylindrical solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention;

FIGS. 7A-7K illustrate a manufacturing process for turning an electroded dielectric film laminate into a solid dielectric elastomer transducer roll, as shown in FIGS. 7I and 7K in accordance with one embodiment of the present invention, where:

FIG. 7A illustrates lamination of dielectric films in accordance with one embodiment of the present invention;

FIG. 7B illustrates cutting a frame away from the dielectric film laminate in accordance with one embodiment of the present invention;

FIG. 7C illustrates removal of the frame from the dielectric film laminate in accordance with one embodiment of the present invention;

FIG. 7D illustrates mounting a carrier plate with the dielectric film laminate on a rolling machine in accordance with one embodiment of the present invention;

FIG. 7E illustrates the process of rolling the dielectric film laminate by moving the carrier plate under a counter rotating scrub roller into a solid roll of dielectric elastomer film in accordance with one embodiment of the present invention;

FIG. 7F illustrates the process of rolling the dielectric film laminate shown in FIG. 7E towards the end of the process in accordance with one embodiment of the present invention;

FIG. 7G illustrates the carrier plate retracting after the rolling process is complete in accordance with one embodiment of the present invention;

FIG. 7H illustrates transfer of a solid dielectric elastomer transducer roll to a cutting fixture for segmenting the roll into individual solid dielectric elastomer transducer rolls shown in FIG. 7G in accordance with one embodiment of the present invention;

FIG. 7I illustrates the solid dielectric elastomer transducer roll segmented into individual solid dielectric elastomer transducer rolls in accordance with one embodiment of the present invention;

FIG. 7J illustrates application of conductive adhesive into a terminal cup for electrically attaching to ends of the solid dielectric elastomer transducer rolls shown in FIGS. 7H and 7I in accordance with one embodiment of the present invention;

FIG. 7K illustrates attaching and curing the terminal cups onto the ends of the solid dielectric elastomer transducer roll shown in FIG. 1 in accordance with one embodiment of the present invention;

FIG. 8 is a detail view of the rolling machine used in steps illustrated in FIGS. 7D-F in accordance with one embodiment of the present invention;

FIG. 9 is a detail view of the cutting fixture for segmenting the solid dielectric elastomer transducer roll into individual solid dielectric elastomer transducer rolls shown in FIGS. 7H and 7J in accordance with one embodiment of the present invention;

FIG. 10 is an end view of an individual segmented solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention after segmentation and prior to exposing the end to a solvent;

FIG. 11 is an end view of an individual segmented solid dielectric elastomer transducer roll after the application of a solvent to cause local swelling and separation of the layers in accordance with one embodiment of the present invention;

FIG. 12 illustrates a motion control system for controlling the rolling process of rolling up a solid dielectric elastomer transducer roll with a carrier plate under a scrub roller as illustrated in FIGS. 7D-F and FIG. 8 in accordance with one embodiment of the present invention;

FIG. 13 illustrates a simplified motion control system for the rolling process illustrated in FIGS. 7D-F and FIG. 8 where slip can occur between the scrub roller and a growing solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention;

FIG. 14 illustrates a textile covering positioned over an outside surface of the scrub roller illustrated in FIG. 13 in accordance with one embodiment of the present invention;

FIG. 15 is a detailed view of the textile covering illustrated in FIG. 14 in accordance with one embodiment of the present invention;

FIG. 16 illustrates circumferential lengthening of outer layers of solid dielectric elastomer transducer roll caused by rolling a pre-strained dielectric elastomer film with excessive pre-strain during the rolling process;

FIG. 17 illustrates a wrinkle mechanism in the loosely packed space between individual solid dielectric elastomer transducer rolls in accordance with one embodiment of the present invention;

FIG. 18 illustrates an electrode pattern with overlap regions to provide support in bands between solid dielectric elastomer transducer rolls to prevent wrinkles that would otherwise start in the overlapping regions;

FIG. 19 illustrates a non-limiting example fixture for positioning electrical terminal caps on ends of a solid dielectric elastomer transducer roll during curing;

FIG. 20 illustrates a derivation model of a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention;

FIG. 21 is a graphical illustration depicting force provided by each additional ring in a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention;

FIG. 22 is a graphical illustration depicting capacitance change versus axial displacement of a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention;

FIG. 23 is a graphical illustration depicting blocked force versus applied voltage response of a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention;

FIG. 24 is a graphical illustration depicting blocked force versus axial displacement showing the difference between the solid dielectric elastomer transducer roll in compression versus tension in accordance with one embodiment of the present invention;

FIG. 25 is a graphical illustration of blocked force versus longitudinal displacement showing the difference between the solid dielectric elastomer transducer roll in compression versus tension in accordance with one embodiment of the present invention;

FIG. 26 is a graphical representation of stiffness of solid dielectric elastomer transducer rolls in accordance with one embodiment of the present invention;

FIG. 27 illustrates a solid dielectric elastomer transducer roll in flat roll mode where the roll is placed under compression in a radial direction rather than in an axial direction in accordance with one embodiment of the present invention;

FIG. 28 illustrates a geometric model of a solid dielectric elastomer transducer roll in flat roll mode where the roll is placed under compression in a radial direction in accordance with one embodiment of the present invention;

FIG. 29 is a graphical illustration depicting stretch ratio versus percent compression in a radial direction of a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention;

FIG. 30 illustrates a static equilibrium diagram of a solid dielectric elastomer transducer roll in flat roll mode under static load in accordance with one embodiment of the present invention;

FIG. 31 is a graphical illustration depicting capacitance versus compression in a radial direction of a solid dielectric elastomer transducer roll in flat roll mode in accordance with one embodiment of the present invention;

FIGS. 32A, 32B, 32C and 32D illustrate a solid dielectric elastomer transducer roll under increasing compression force in a radial direction in accordance with one embodiment of the present invention;

FIG. 33 illustrates a finite element analysis model of a solid dielectric elastomer transducer roll undergoing radial compression in accordance with one embodiment of the present invention; and

FIG. 34 illustrates the delamination of a solid dielectric elastomer transducer roll undergoing radial compression in accordance with one embodiment of the present invention.

Variation of the invention from that shown in the figures is contemplated.

DETAILED DESCRIPTION OF THE INVENTION

Examples of electroactive polymer devices and their applications are described, for example, in U.S. Pat. Nos. 6,343,129; 6,376,971; 6,543,110; 6,545,384; 6,583,533; 6,586,859; 6,628,040; 6,664,718; 6,707,236; 6,768,246; 6,781,284; 6,806,621; 6,809,462; 6,812,624; 6,876,135; 6,882,086; 6,891,317; 6,911,764; 6,940,221; 7,034,432; 7,049,732; 7,052,594; 7,062,055; 7,064,472; 7,166,953; 7,199,501; 7,199,501; 7,211,937; 7,224,106; 7,233,097; 7,259,503; 7,320,457; 7,362,032; 7,368,862; 7,378,783; 7,394,282; 7,436,099; 7,492,076; 7,521,840; 7,521,847; 7,567,681; 7,595,580; 7,608,989; 7,626,319; 7,750,532; 7,761,981; 7,911,761; 7,915,789; 7,952,261; 8,183,739; 8,222,799; 8,248,750; and in U.S. Patent Application Publication Nos.; 2007/0200457; 2007/0230222; 2011/0128239; and 2012/0126959, the entireties of which are incorporated herein by reference.

In various embodiments, the present invention provides various improvements over conventional hollow rolled dielectric elastomer transducers and manufacturing processes for making those transducers. Embodiments of the present invention overcome these drawbacks by winding dielectric elastomer films into a solid roll that does not waste space or collapse as turns are added. A rolling machine also is disclosed, along with a manufacturing process, materials, and fixtures for manufacturing dielectric elastomer actuator rolls with the machine, as described herein in the detailed description of the invention section of the present disclosure.

The various embodiments discussed hereinbelow in connection with FIGS. 1-19 provide a dielectric elastomer transducer rolls formed by rolling laminated films into a compact spiral, which will be referred to herein as “solid.” Multiple individual solid dielectric elastomer transducer rolls may be produced by segmented cutting of the transducer rolls, where the cutting affords electrical connections to the ends of the rolls. A conductive adhesive formulated with solvent may be used to swell the ends of the roll to improve mechanical and electrical connection of the rolls to the terminals. Also provided is a rolling machine for dielectric elastomer actuators comprised of a scrub roller that counter-rotates with respect to an advancing plate. Another rolling machine is provided in which motion control is simplified by spinning the scrub roller faster than the carrier plate advances. A non-stick textile cover for the scrub roller is provided to minimize adhesion by minimizing contact area through the use of knit threads that can locally deflect to minimize contact stress. An electrode pattern is also provided for transducer rolls in which electrodes overlap to support areas of the roll that could otherwise buckle and initiate wrinkles. Also provided are novel fixtures for cutting the roll and adhering terminals, to be used in conjunction with the rolling machine.

The solid transducer rolls overcome buckling problems that normally would limit the number of turns that can be added to a hollow type transducer roll. Solid transducer rolls also save space that is wasted by the hollow type rolls known in the art. A rolling machine forms solid rolls with geometric tolerances finer than hand-rolling, at greater speed and lower cost. A compliant, textile, non-stick cover for the scrub roller in the machine simplifies motion control and reduces machine cost. An overlapping electrode pattern prevents wrinkles.

FIG. 1 illustrates a solid dielectric elastomer transducer roll 100 in accordance with one embodiment of the present invention. The solid dielectric elastomer transducer roll 100 comprised of two layers of dielectric film 102, 104, one of which has been patterned with one or more layers of electrodes 106, 108 on both sides. The layers of dielectric film 102, 104 are wound together into a tight solid spiral cylinder. The area 110 in which the electrodes 106, 108 overlap acts as a dielectric elastomer transducer. Electrical connection to the two plates of the capacitor can be made where the electrodes 106, 108 meet the ends of the cylinder. The electrodes 106, 108 are offset relative to each other to provide electrical connection at the ends 112, 114 of the solid dielectric elastomer transducer roll 100 such that the first electrode 106 is accessible at the top 112 and the second electrode 108 is accessible at the bottom 114 of the transducer 100. Although in the illustrated embodiment, the solid dielectric elastomer transducer roll 100 has a right circular cylindrical form, other forms are contemplated such as triangular, square, rectangular, among other polyhedral forms.

FIG. 2 illustrates tension σ_(p) that accumulates when removing film 120 from a liner 122 while winding a hollow 124 rolled dielectric elastomer transducer 126. Some peeling stress o is unavoidable when removing the film 120 having a thickness “t” from the liner 122.

FIG. 3 illustrates radial stress ΔP developed in the hollow rolled dielectric elastomer transducer 126 shown in FIG. 2 caused by the tension σ_(p) created when the film 120 is peeled from the liner 122 (not shown). Radial stress ΔP (pressure) in the compressed layers below must support the tension of each new wrap.

FIG. 4 is a graphical illustration depicting the accumulation of radial stress ΔP in the hollow rolled dielectric elastomer transducer 126 shown in FIG. 2 as additional wraps are added to the hollow rolled dielectric elastomer transducer 126. As more wraps are added the radial stress ΔP (pressure) in the center increases. If the force becomes large enough, the inner layers may delaminate and buckle, like an arch collapsing. As indicated by the radial stress ΔP [Pa] versus radial distance [m] curve 130 in graph 128, the radial stress ΔP on the innermost layer 132 is much higher than the radial stress ΔP on the outermost layer 134.

In the context of FIGS. 2-4, the peel stress σ_(p) and strain in a single layer of dielectric film 120 are given below for values typical of a dielectric elastomer coating:

$\begin{matrix} {\sigma_{p} = {\frac{\sigma_{PEEL}}{t} = {\frac{\left\lbrack {3.8\mspace{14mu} N\text{/}m} \right\rbrack}{\left\lbrack {{80\mspace{11mu} E} - {6\mspace{11mu} m}} \right\rbrack} = {0.048\mspace{14mu} {MPa}}}}} & {{Eq}.\mspace{11mu} 1} \\ {s = {\frac{\sigma_{p}}{Y} = {\frac{\left\lbrack {0.048\mspace{14mu} {MPa}} \right\rbrack}{\left\lbrack {0.6\mspace{14mu} {MPa}} \right\rbrack} = {0.08 = {8\% \mspace{14mu} {strain}}}}}} & {{Eq}.\mspace{11mu} 2} \end{matrix}$

The force balance for a half-wrap of film, as shown in FIG. 3, can be solved for the radial stress ΔP.

$\begin{matrix} {{\sum F_{z}} = {{{{- 2}\sigma_{p}t\; } + {2\; r\; \; \Delta \; P}} = 0}} & {{Eq}.\mspace{11mu} 3} \\ {{\Delta \; P} = {\frac{\sigma_{p}t}{r} = \frac{\sigma_{PEEL}}{r}}} & {{Eq}.\mspace{11mu} 4} \end{matrix}$

The radial stress ΔP in layer “i” is due to the accumulated stress of the layers above it as given in the equation below. For typical values of peel stress σ_(p) on a hollow rolled dielectric elastomer transducer 126 with 1 mm internal radius, the calculated pressures have been plotted in FIG. 4.

$\begin{matrix} {P_{i} = {{\Delta \; P_{i}} + {\sum\limits_{0}^{i}{\Delta \; P}}}} & {{Eq}.\mspace{11mu} 5} \end{matrix}$

FIG. 5 illustrates inner windings 132 of the hollow rolled dielectric elastomer transducer 126 that have collapsed under the accumulated radial stress P imposed by tension σ_(p) in the outer windings 134. This “collapsing of the inner layers” problem with the conventional hollow rolled dielectric elastomer transducer 126 provides the motivation for the present inventors' development of the solid dielectric elastomer transducer roll 100 shown in FIG. 6.

FIG. 6 illustrates a cylindrical solid dielectric elastomer transducer roll 100 in accordance with one embodiment of the present invention. The cylindrical solid dielectric elastomer transducer roll 100 does not exhibit a collapse of the inner layers 136 under the accumulated radial stress P imposed by tension σ_(p) in the outer windings 138.

FIGS. 7A-7K illustrate a manufacturing process for turning an electroded dielectric film laminate 101 into a solid dielectric elastomer transducer roll 178, as shown in FIGS. 7I and 7K in accordance with one embodiment of the present invention. The process rolls the dielectric film laminate 101 into a tight spiral without an opening extending axially in the center of the solid dielectric elastomer transducer roll 178.

FIG. 7A illustrates a step of the process where two dielectric films 102, 104 are laminated 150 in accordance with one embodiment of the present invention. The first dielectric film 102 comprises a first electrode layer 106 on a top portion and a second electrode layer 108 on a bottom portion. The first dielectric film 102 with the electrodes 106, 108 patterned on both sides thereof are held in tension (pre-stressed) in a rigid frame 152. The first film 102 with the frame 152 is then laminated to the second dielectric film 104 while it is still attached to the liner 154 used to coat it. The electroded dielectric film laminate 101 (not shown in FIG. 7A) comprising the laminated films 102, 104 is positioned on a carrier plate 156, which will be used to hold the dielectric film laminate 101 during the rolling process.

FIG. 7B illustrates another step of the process where the frame 152 is cut 158 away from the dielectric film laminate 101 (not shown in FIG. 7B) in accordance with one embodiment of the present invention. The cut path 160 is inside the inner perimeter of the frame 152.

FIG. 7C illustrates another step of the process where the frame 152 is removed 162 from the dielectric film laminate 101 in accordance with one embodiment of the present invention.

FIG. 7D illustrates another step of the process where the carrier plate 156 with the dielectric film laminate 101 is mounted 164 on a rolling machine 166 in accordance with one embodiment of the present invention. The rolling machine 166 comprises a scrub roller 168, which rolls up the dielectric film laminate 101.

FIG. 7E illustrates another step in the process where the dielectric film laminate 101 on the carrier plate 156 is rolled into a solid roll of dielectric elastomer film under a counter rotating 172 scrub roller 168 as the carrier plate 156 is moved 170 in direction 174 by a conveyor or other suitable drive mechanism in accordance with one embodiment of the present invention. As the dielectric film laminate 101 is rolled, it is released from the liner 154. The process continues until the entire dielectric film laminate 101 is rolled. FIG. 7F illustrates the process of rolling the dielectric film laminate 101 shown in FIG. 7E towards the end of the process in accordance with one embodiment of the present invention.

FIG. 7G illustrates another step of the process where the carrier plate 156 is retracted 176 in direction 177 after the rolling process is complete in accordance with one embodiment of the present invention. As shown, a solid dielectric elastomer transducer roll 178 is provided at the end of this step.

FIG. 7H illustrates another step in the process where the solid dielectric elastomer transducer roll 178 is transferred 180 to a cutting fixture 182 for segmenting the roll 178 with a cutter 184, such as a blade or slitter, into individual solid dielectric elastomer transducer rolls shown in FIG. 7G in accordance with one embodiment of the present invention.

FIG. 7I illustrates another step in the process where the solid dielectric elastomer transducer roll 178 is segmented 186 into individual solid dielectric elastomer transducer rolls 178 a, 178 b, and 178 c in accordance with one embodiment of the present invention.

FIG. 7J illustrates another step in the process where a conductive adhesive 192 is applied 190 into an electrical terminal 194 having a cup shape for electrically attaching to ends of the solid dielectric elastomer transducer rolls 178 a, 178 b, and 178 c shown in FIGS. 7H and 7I in accordance with one embodiment of the present invention.

FIG. 7K illustrates another step in the process where terminals 194 a ₁, 194 a 2 are attached and cured 196 onto the ends of the solid dielectric elastomer transducer roll 178 a, terminals 194 b ₁, 194 b ₂ are attached and cured 196 onto the ends of the solid dielectric elastomer transducer roll 178 b, and terminals 194 c ₁, 194 c ₂ are attached and cured 196 onto the ends of the solid dielectric elastomer transducer roll 178 c in accordance with one embodiment of the present invention.

FIG. 8 is a detail view of the rolling machine 166 used in the steps illustrated in FIGS. 7D-G in accordance with one embodiment of the present invention.

FIG. 9 is a detail view of the cutting fixture 182 for segmenting the solid dielectric elastomer transducer roll 178 into individual solid dielectric elastomer transducers rolls 178 a, 178 b, and 178 c shown in FIGS. 7I and 7J in accordance with one embodiment of the present invention. The cutting fixture 182 comprises a movable jaw 196 and a fixed jaw 198. The movable jaw comprises alignment slots 202 and the fixed jaw comprises alignment slots 204, which are aligned with the alignment slots 202 of the movable jaw 202. The cutting fixture comprises an aperture for receiving the solid dielectric elastomer transducer roll 178 therein. The movable jaw 196 moves relative to the fixed jaw 198 to define a longitudinal aperture 200 for receiving and holding the solid dielectric elastomer transducer roll 178 in place during the segmenting process. The cutter 184 is advanced through the alignment slots 202 in the movable jaw 196, through the solid dielectric elastomer transducer roll 178, and the alignment slots 204 in the fixed jaw 198. The clamping action of the jaws 196, 198 also straightens the solid dielectric elastomer transducer roll 178 within the aperture 200 in preparation for segmentation.

FIG. 10 is an end view of an individual segmented solid dielectric elastomer transducer roll 100 in accordance with one embodiment of the present invention after segmentation and prior to exposing the end to a solvent.

FIG. 11 is an end view of an individual segmented solid dielectric elastomer transducer roll 100′ after the application of a solvent to the end to cause local swelling and separation of the layers 206, 208, and 210 in accordance with one embodiment of the present invention. This improves penetration of the conductive adhesive 192, shown in FIG. 7J. During the curing process 196 shown in FIG. 7K, the solvent evaporates, leaving inter-digitated glue that makes a robust electrical and mechanical connection between the capping end-terminal 194 shown in FIGS. 7J and 7K and the electrodes 106, 108 of the solid dielectric elastomer transducer roll 100. In one embodiment, the electrically conductive adhesive 192 may be formulated with a solvent that swells the ends of the roll 100 to improve mechanical and electrical connection of the rolls 100 to the terminals 194.

FIG. 12 illustrates a motion control system 212 for controlling the process of rolling the dielectric film laminate 101 into a solid dielectric elastomer transducer roll 178 with the rolling machine 166. The scrub roller 168 portion of the rolling machine 166 has a radius r_(scrub). The motion control system 212 may be any electronic processor or digital logic based programmable motion controller configured to control the velocity and direction of rotation of the scrub roller 168 and the velocity and direction of translation of the carrier plate 156 in accordance with the present invention. As previously discussed in connection with FIGS. 7D-G, the carrier plate 156 is advanced in direction 174 at velocity V_(plate) while the scrub roller 168 is rotated in a counter direction 172 at velocity V_(scrub). As the outer surface of the scrub roller 168 contacts the dielectric film laminate 101, the dielectric film laminate 101 begins to roll up to form the solid dielectric elastomer transducer roll 178. The solid dielectric elastomer transducer roll 178 grows in diameter until the carrier plate 156 reaches the end of stroke. As matching the speeds of the carrier plate 156 and the scrub roller 168 can improve the rolling process and excess speed on the carrier plate 156 can jam the solid dielectric elastomer transducer roll 178 under the scrub roller 168. On the other hand, if the solid dielectric elastomer transducer roll 178 is sticky and adheres to the scrub roller 168, excess velocity on the scrub roller 168 can lift the solid dielectric elastomer transducer roll 178 off the liner 154 and wrap it around the scrub roller 168. Each of these situations can result in damaging the solid dielectric elastomer transducer roll 178. Accordingly, the motion control system 212 may be programmed in accordance with the following considerations to provide various levels of control ranging from the simple to the complex.

By way of example, the motion control system 212 may be configured in various forms from a relatively simple control system to a more complex control system. In one embodiment, the control system 212 may be configured to match the velocity of the carrier plate 156 V_(plate) in direction 174 and the velocity of the scrub roller 168 V_(scrub) in direction 172 such that |V_(plate)|=|V_(scrub)|. In another embodiment, the motion control system 212 may be configured to account for the velocity of the transducer roll V_(roll) in direction 214 as a new variable to compensate for the movement of the center of the solid dielectric elastomer transducer roll 178 as the diameter grows such that |V_(plate)|−|V_(roll, x)|=k|V_(scrub)|. In yet another embodiment, the motion control system 212 may be configured to account for a stretch coefficient “k” to compensate for stretching of the dielectric film laminate 101 as it is peeled from the liner 154 such that |V_(plate)|−|V_(roll, x)|=k|V_(scrub)|. Finally, in another embodiment, the motion control system 212 may be configured to employ at least one sensor to sense force and provide a closed loop feedback mechanism to the motion control system 212.

The complexity of the various configurations of the motion control system 212 outlined above can be avoided if the solid dielectric elastomer transducer roll 178 does not stick to the scrub roller 168. In that case, the scrub roller 168 can be rotated quickly relative to the carrier plate 156 so that it always brushes the solid dielectric elastomer transducer roll 178 back, as illustrated below in FIG. 13.

FIG. 13 illustrates a simplified implementation of the motion control system 212 that is configured to account for slip 218 that can occur between the scrub roller 168 and the growing diameter of the solid dielectric elastomer transducer roll 178. Accordingly, the motion control system 212 may be configured to control the velocity of the carrier plate 156 V_(plate) in direction 174 relative to the velocity of the scrub roller 168 V_(scrub) in direction 172 such that |V_(plate)|<<|V_(scrub)|.

FIG. 14 illustrates a textile covering 222 positioned over an outside surface of the scrub roller 168 illustrated in FIG. 13. The textile covering 222 is made of a non-stick material to provide non-stick contact between the scrub roller 168 and the solid dielectric elastomer transducer roll 178 in accordance with one embodiment of the present invention. FIG. 15 is a detailed view of the textile covering 222 provided over the outside surface of the scrub roller 168 as illustrated in FIG. 14 in accordance with one embodiment of the present invention. With reference to FIGS. 14 and 15, a suitable non-stick contact between the scrub roller 168 and the solid dielectric elastomer transducer roll 178 may be achieved by covering the scrub roller with a knit fabric 222. The knit fabric 222 minimizes the dielectric-to-roller contact area and thus minimizes the adhesion force. The knit fabric 222 insures that the contact area is primarily empty air. Because the knit fibers can deflect, stress concentrations on the solid dielectric elastomer transducer roll 178 film are smaller than those provided by, for example, a roller made of a hard grooved plastic. This protects the solid dielectric elastomer transducer roll 178 from mechanical damage during the rolling process.

FIG. 16 illustrates circumferential lengthening of outer layers of the dielectric elastomer transducer roll 224 caused by rolling a pre-strained dielectric elastomer film with excessive pre-strain during the rolling process. An advantage of the rolling process according to one embodiment of present invention is the ability to apply a minimum of pre-strain to the dielectric elastomer transducer roll during the rolling process. In one aspect, the minimum pre-strain is only the pre-strain required for peeling the dielectric film laminate from the liner during the rolling process. This is useful because excessive pre-strain can cause relaxation of longitudinal pre-strain that can lead circumferential lengthening of the outer layers 226 of the transducer roll 224. As shown in FIG. 16, the outer layers 224 of the transducer roll 224 have delaminated in some places and not others, causing buckling. So, even if the inner layers of the transducer roll 224 do not buckle, the outer layers 224 may slip. This problem with pre-strain may be minimized by rolling up the unstrained dielectric film laminate directly from the liner on which it was coated in accordance with one embodiment of the present invention.

FIG. 17 illustrates a wrinkling mechanism in the loosely packed space between individual electroded solid dielectric elastomer transducer rolls 178 a, 178 b in accordance with one embodiment of the present invention. The bands 226 of un-electroded film in between electroded solid dielectric elastomer transducer rolls 178 a, 178 b can cause rolling problems. The dielectric layers in these bands 226 are supported only loosely by underlying layers, and can therefore buckle 228 in response to non-uniform rotation along the length of the roll 168. This is illustrated in FIG. 17, where the electroded solid dielectric elastomer transducer rolls 178 a, 178 b have undergone slightly different rotation relative to the rotation rates of the band 226 therebetween. The electroded solid dielectric elastomer transducer rolls 178 a, 178 b portions of the transducer roll 178 are supported by the electrodes whereas the band 226 therebetween is unsupported and can buckle. The force of peeling the laminate film from the liner can also produce V-shaped wrinkles in these bands 226. The wrinkles propagate along the length of the roll as turns are added, which is undesirable. To minimize this problem, the regions of adjacent electroded solid dielectric elastomer transducer rolls 178 a, 178 b can be overlapped as described hereinbelow in FIG. 18.

FIG. 18 illustrates an electrode pattern 230 with overlapping regions 232 to provide support in bands between adjacent (juxtaposed) layers of electrode materials to be segmented into individual solid dielectric elastomer transducer rolls 178 a, 178 b. The electrode pattern 230 prevents wrinkles that would otherwise start in the overlapping regions 232 and also enables segmenting the roll into individual solid dielectric elastomer transducer rolls 178 a, 178 b. The first dielectric film 102 is shown delaminated from the second dielectric film 104 for illustration purposes. As shown, the first and second electrodes 106, 108 are applied on opposite sides of the dielectric film 102 in a staggered (offset) manner to create overlapping regions 232. A first side of the dielectric film 102 includes multiple layers of electrode 106 ₁, 106 ₂, and 106 ₃ material juxtaposed relative to each other and spaced apart by a gap 235 therebetween. A second side of the dielectric film 102 includes multiple layers of electrode 108 ₁, 108 ₂, and 108 ₃ material juxtaposed relative to each other and spaced apart by a gap 237 therebetween. The layers of electrodes 106 ₁, 106 ₂, and 106 ₃ on the first side of the dielectric film 102 are offset or staggered from the layers of electrodes 108 ₁, 108 ₂, 108 ₃ on the second side of the dielectric film 102 to create the overlapping regions 232 ₁, 232 ₂ and so on. The second dielectric film 104 is still releasably attached to the liner 154 which is attached to the carrier plate 156. As previously discussed, the first dielectric film 102 with the electrodes 106 ₁, 106 ₂, 106 ₃, 108 ₁, 108 ₂, and 108 ₃ formed on each side thereof is laminated to the second dielectric film 104 on the liner 154.

FIG. 19 illustrates a non-limiting example of fixture 234 for positioning the electrical terminal caps 194 a ₁, 194 a ₂ on ends of a solid dielectric elastomer transducer roll 178 a during curing. The fixture 234 comprises a slot 236 to receive the solid dielectric elastomer transducer roll 178 a and blade terminals 238 for receiving the electrical terminal caps 194 a ₁, 194 a ₂. As previously discussed in FIGS. 7I and 7J, the electrical terminal caps 194 a ₁, 194 a ₂ are filled with an electrically conductive adhesive 192. The ends of the solid dielectric elastomer transducer roll 178 a are then inserted into each one of the conductive adhesive 192 filled electrical terminal caps 194 a ₁, 194 a ₂ and then a cam 240 is used to apply a clamping force to the assembled solid dielectric elastomer transducer roll 178 a and conductive adhesive 192 filled electrical terminal caps 194 a ₁, 194 a ₂ during the curing process.

Having described embodiments of solid dielectric elastomer transducer rolls, methods for manufacturing the solid dielectric elastomer transducer rolls, and machines for manufacturing the solid dielectric elastomer transducer rolls, the specification now turns to a description of capacitance models for a solid dielectric elastomer transducer roll in axial tension and compression modes as well as radial (flat mode) compression modes.

FIG. 20 illustrates a derivation model 300 of a solid dielectric elastomer transducer roll 302, similar to the solid dielectric elastomer transducer roll 100, 178 described above, in accordance with one embodiment of the present invention. The diagram depicted in FIG. 20 shows the solid dielectric elastomer transducer roll 302 in a relaxed state and also shows a comparison of an outer ring 304 of the solid dielectric elastomer transducer roll 302 in a relaxed state and the outer ring 304′ when it is in tension. The solid dielectric elastomer transducer roll 302 has a length x_(o) when the solid dielectric elastomer transducer roll 302 is not in tension and a length (x_(o)+x) or λx_(o) when tensioned. The model assumes the spiral equivalent of N rings and the volume inside each ring is conserved due to the incompressibility of the rings within and the volume of the ring itself is conserved. Each ring is an annular capacitor and the total capacitance is the sum of the all N rings.

The main equations developed in accordance with the model are:

Effective Number of Rings in Roll $N = \left( \frac{y_{0}}{t_{0}\pi} \right)^{1/2}$ Eq. 6 Blocked Force $F_{total} = {V^{2}{\pi ɛɛ}_{0}{\sum\limits_{n = 1}^{N}\left( {{\ln \left( {n + 1} \right)} - {\ln (n)}} \right)^{- 1}}}$ Eq. 7 Spring Rate k = Y(y₀ + y_(p))t₀/(x₀ + x_(p)) Eq. 8 Free Stroke ${\Delta x} \cong \frac{F_{total}}{k}$ Eq. 9 Roll Diameter D_(composite) = 2N(t_(film) + t_(elec)) Eq. 10

A Spiral is Equivalent to N Rings

The outer ring 304 of the un-tensioned solid dielectric elastomer transducer roll 302 has an outer radius b_(o) that is equal to the N rings of thickness t_(o):

b ₀ =Nt ₀  Eq. 11

The area of the film is same whether it is laid out flat (y_(ot)) or rolled up into a circle (πb² _(o)):

$\begin{matrix} \begin{matrix} {A_{film} = {y_{0}t}} \\ {= {\pi \; b_{0}^{2}}} \end{matrix} & \left( {{Eq}.\mspace{14mu} 12} \right) \\ {{y_{o}t_{0}} = {\pi \left( {Nt}_{0} \right)}^{2}} & \left( {{Eq}.\mspace{14mu} 13} \right) \\ {{Nt}_{0} = \left( \frac{y_{0}t_{0}}{\pi} \right)^{1/2}} & \left( {{Eq}.\mspace{14mu} 14} \right) \\ {N = \left( \frac{y_{0}}{t_{0}\pi} \right)^{1/2}} & \left( {{Eq}.\mspace{14mu} 15} \right) \end{matrix}$

Volume Inside Each Ring is Conserved

Volume₀=Volume(λ)  Eq. 16

Volume₀ =πa ₀ ² x ₀  Eq. 17

Volume(λ)=πa ²  Eq. 18

πa ₀ ² x ₀ =πa ² λx ₀  Eq. 19

a ₀ ² =a ²λ  Eq. 20

a ²=λ⁻¹ a ₀ ²  Eq. 21

a=λ ^(−½) a ₀  Eq. 22

Volume of Each Ring Itself is Conserved

Volume₀=Volume(λ)  Eq. 23

Volume₀=π(b ₀ ² −a ₀ ²)x ₀  Eq. 24

Volume(λ)=π(b ² −a ²)λx ₀  Eq. 25

π(b ₀ ² −a ₀ ²)x ₀=π(b ² −a ²)λx  Eq. 26

(b ₀ ² −a ₀ ²)=(b ² −a ²)λ  Eq. 27

b ²=λ⁻¹(b ₀ ² −a ₀ ²)+a ²  Eq. 28

b=(λ⁻¹(b ₀ ² −a ₀ ²)+a ²)^(1/2)  Eq. 29

Using the results from Eq. 22, this can be simplified further:

b=(λ⁻¹(b ₀ ² −a ₀ ²)+a ²)^(1/2)  Eq. 30

b=(λ⁻¹(b ₀ ² −a ₀ ²)+(λ−^(1/2) a ₀)₂)  Eq. 31

b=(λ⁻¹(b ₀ ² −a ₀ ²)+λ⁻¹ a ₀ ²)^(1/2)  Eq. 32

b=(λ⁻¹(b ₀ ² −a ₀ ² +a ₀ ²))^(1/2)  Eq. 33

b=(λ⁻¹ b ₀ ²)^(1/2)  Eq. 34

b=λ− ^(1/2) b ₀  Eq. 35

Capacitance of the Annular Capacitor

Initially the capacitance is:

$\begin{matrix} {C_{0} = \frac{2{\pi ɛɛ}_{0}x_{0}}{\ln \left( \frac{b_{0}}{a_{0}} \right)}} & {{Eq}.\mspace{14mu} 36} \end{matrix}$

After it has been stretched it becomes longer, so that the length becomes (λx₀) and the radii (a and b) are no longer the initial radii (a₀ and b₀):

$\begin{matrix} {{C(\lambda)} = \frac{2{\pi ɛɛ}_{0}x_{0}\lambda}{\ln \left( \frac{b}{a} \right)}} & {{Eq}.\mspace{14mu} 37} \end{matrix}$

Substituting results from Equations 22 and 35 allows the stretched capacitance to be expressed in terms of initial geometry.

$\begin{matrix} {{C(\lambda)} = \frac{2{\pi ɛɛ}_{0}x_{0}\lambda}{\ln \left( \frac{b}{a} \right)}} & {{Eq}.\mspace{14mu} 38} \\ {{C(\lambda)} = \frac{2{\pi ɛɛ}_{0}x_{0}\lambda}{\ln \left( \frac{\lambda^{{- 1}/2}b_{0}}{\lambda^{{- 1}/2}a_{0}} \right)}} & {{Eq}.\mspace{14mu} 39} \\ {{C(\lambda)} = {\frac{2{\pi ɛɛ}_{0}x_{0}}{\ln \left( \frac{b_{0}}{a_{0}} \right)}\lambda}} & {{Eq}.\mspace{14mu} 40} \end{matrix}$

Capacitance is expected to vary linearly with the stretch ratio. To get the force each ring provides note that electrostatic force depends on the change in capacitance with excursion from rest.

$\begin{matrix} {F_{elec} = {V^{2}\frac{\partial C}{\partial x}}} & {{Eq}.\mspace{14mu} 41} \end{matrix}$

Note that the stretch ratio can be expressed in terms of that excursion from rest.

$\begin{matrix} {\lambda = {1 + \frac{x}{x_{0}}}} & {{Eq}.\mspace{14mu} 42} \\ {{C(x)} = {\frac{2{\pi ɛɛ}_{0}x_{0}}{\ln \left( \frac{b_{0}}{a_{0}} \right)}\left( {1 + \frac{x}{x_{0}}} \right)}} & {{Eq}.\mspace{14mu} 43} \end{matrix}$

The derivative cancels out the initial length of the actuator (x₀). This means that the electric force will not be predicted to change as the length of the actuator changes.

$\begin{matrix} {\frac{\partial C}{\partial x} = \frac{2{\pi ɛɛ}_{0}x_{0}}{x_{0}{\ln \left( \frac{b_{0}}{a_{0}} \right)}}} & {{Eq}.\mspace{14mu} 44} \\ {\frac{\partial C}{\partial x} = \frac{2{\pi ɛɛ}_{0}}{\ln \left( \frac{b_{0}}{a_{0}} \right)}} & {{Eq}.\mspace{14mu} 45} \\ \begin{matrix} {F_{elec} = {\left( {1/2} \right)V^{2}\frac{\partial C}{\partial x}}} \\ {= \frac{V^{2}{\pi ɛɛ}_{0}}{\ln \left( \frac{b_{0}}{a_{0}} \right)}} \end{matrix} & {{Eq}.\mspace{14mu} 46} \end{matrix}$

Note that the outer radius b₀ is just the inner radius (a₀) plus the thickness of the film (t₀).

$\begin{matrix} \begin{matrix} {F_{elec} = {\left( {1/2} \right)V^{2}\frac{\partial C}{\partial x}}} \\ {= \frac{V^{2}{\pi ɛɛ}_{0\;}}{\ln \left( \frac{a_{0} + t}{a_{0}} \right)}} \end{matrix} & {{Eq}.\mspace{14mu} 47} \end{matrix}$

To get the total force we must sum up the contributions of all N of the rings. Note that each ring has an outer radius that is one thickness greater than the inner radius.

$\begin{matrix} {F_{total} = {V^{2}{\pi ɛɛ}_{0}{\sum\limits_{n = 1}^{N}\left( {\ln \left( \frac{\left( {n + 1} \right)t_{0}}{{nt}_{0}} \right)} \right)^{- 1}}}} & {{Eq}.\mspace{14mu} 48} \end{matrix}$

Canceling Like Terms

$\begin{matrix} {F_{total} = {V^{2}{\pi ɛɛ}_{0}{\sum\limits_{n = 1}^{N}\left( {\ln \left( \frac{\left( {n + 1} \right)}{n} \right)} \right)^{- 1}}}} & {{Eq}.\mspace{14mu} 49} \\ {F_{total} = {V^{2}{\pi ɛɛ}_{0}{\sum\limits_{n = 1}^{N}\left( {{\ln \left( {n + 1} \right)} - {\ln (n)}} \right)^{- 1}}}} & {{Eq}.\mspace{14mu} 50} \end{matrix}$

The thickness of a layer has not, in fact, disappeared. It appears in the upper limit of the series (N). The total number of layers (N) can be expressed simply in terms of the initial geometry.

$\begin{matrix} {{{F_{total} = {V^{2}{\pi ɛɛ}_{0\;}{\sum\limits_{n = 1}^{N}\left( {{\ln \left( {n + 1} \right)} - {\ln (n)}} \right)^{- 1}}}},{where}}{N = \left( \frac{y_{0}}{t_{0}\pi} \right)^{1/2}}} & {{Eq}.\mspace{14mu} 51} \end{matrix}$

The expected capacitance change is the force expression (Eq. 51) without the Voltage term ½ V²:

$\begin{matrix} {{{\frac{\partial C}{\partial x} = {2{\pi ɛɛ}_{0}{\sum\limits_{n = 1}^{N}\left( {{\ln \left( {n + 1} \right)} - {\ln (n)}} \right)^{- 1}}}},{where}}{N = \left( \frac{y_{0}}{t_{0}\pi} \right)^{1/2}}} & {{Eq}.\mspace{14mu} 52} \end{matrix}$

Both of the above are measurable. A candidate example geometry includes 48.8603 rings or approximately 49 rings. Accordingly, for approximately 49 rings, a predicted force and capacitance change rate is:

$\begin{matrix} {\mspace{85mu} {F_{elec} = {{\pi ɛɛ}_{0}V^{2}{\sum\limits_{n = 1}^{N}\left( {{\ln \left( {n + 1} \right)} - {\ln (n)}} \right)^{- 1}}}}} & {{Eq}.\mspace{14mu} 53} \\ {F_{elec} = {{{{\pi \lbrack 2.85\rbrack}\left\lbrack {{8.854E} - {12\mspace{14mu} F\text{/}m}} \right\rbrack}\left\lbrack {1200V^{2}} \right\rbrack}{\sum\limits_{n = 1}^{49}\left( {{\ln \left( {n + 1} \right)} - {\ln (n)}} \right)^{- 1}}}} & {{Eq}.\mspace{14mu} 54} \\ {\mspace{79mu} {\frac{\partial C}{\partial x} = {{{\pi \lbrack 2.85\rbrack}\left\lbrack {{8.854E} - {12\mspace{14mu} F\text{/}m}} \right\rbrack}{\sum\limits_{n = 1}^{49}\left( {{\ln \left( {n + 1} \right)} - {\ln (n)}} \right)^{- 1}}}}} & {{Eq}.\mspace{14mu} 55} \end{matrix}$

FIG. 21 is a graphical illustration 306 depicting force 308 provided by each additional ring in a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention. Force [N] is shown along the vertical axis and ring number is shown along the horizontal axis. Accordingly, the additional force 308 provided by each ring grows linearly with the ring number. This is in conformity with expectations, as the area of each ring scales linearly with circumference. The total force of 0.1426 N approximately matches the total force for a model based on simpler assumptions: i.e., dielectric stacked, not rolled, (Eq. 56).

The calculation for parallel layers, not rolled up provides:

$\begin{matrix} \begin{matrix} {F_{elec} = {\left( {1/2} \right)V^{2}\frac{\partial C}{\partial x}}} \\ {= {\left( {1/2} \right)\frac{V^{2}{ɛɛ}_{0}y_{i}}{z_{i}}}} \end{matrix} & {{Eq}.\mspace{14mu} 56} \end{matrix}$

Accordingly, the model provides a measurable prediction for capacitance change:

dC/dx=Ftot/(0.5*(1200̂2))=1.9806e-007 [F/m]

FIG. 22 is a graphical illustration 310 depicting capacitance change versus axial displacement of a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention. Capacitance C[F] is shown along the vertical axis and axial displacement x[mm] is shown along the horizontal axis. The data substantially agrees with the model. In the graphical illustration 310 capacitance change in two solid dielectric elastomer transducer rolls with 10 mm active length are depicted by curves 312 and 14 mm total length are depicted by curves 314. A peak dC/dx of 8.91E-8 F/m was observed when the transducer rolls were in tension. Although this is just (8.9E-8/1.9806E-7)=44% of the expected dC/dx, the active area did not really experience all of the displacement. Some of the displacement was taken up by deformation in the passive 4 mm of the solid dielectric elastomer transducer roll. To estimate the effect that this compliance will have on measured dC/dx, two cases may be considered (1) negligible electrode stiffness and (2) a relatively large electrode stiffness, for example equal to the film stiffness.

Case 1—Electrode Negligible

Assuming that the active and passive areas have equal stiffness (that is, electrode is negligible), then the observed dC/dx is scaled by (total:active=14 mm:10 mm). The observed dC/dx is then (14/10)*([8.9E-8 F/m]/[1.9806E-7 F/m])=63% of expected.

Case 2—Electrode Stiff

If the stiffness of the electrode is not negligible, then it must be taken into account. In planar devices, it may be observed that a standard electrode coating on two sides of a film increases pseudo-DC stiffness of a film by an amount equivalent to multiplying Young's modulus of the film by two. The roll is comprised of two compliances in series. The active Area is 10 mm long and has two layers of electrode, and the passive 4 mm long and has one layer.

s1=0.010m/(2*Y_film*Area)

s2=0.004m/(1.5*Y_film*Area)

And the proportion of deformation occurring in the active area is

Δx ₁ /Δx _(tot)=(5/(5+2.6667)=0.6522.

Scaling by this factor, dC/dx is found to be ((1/0.6522)*[8.9E-8 F/m])/[1.98E-7 F/m]=69% of expected. In the absence of control data measuring electrode stiffness directly, this provides the best estimate of how the observed capacitance change relates to the nested ring model.

FIG. 23 is a graphical illustration 316 depicting blocked force versus applied voltage response 318 of a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention. The response 318 was obtained by measuring a sample on an INSTRON instrument for measuring tension/compression, made by INSTRON of Norwood, Mass., at 1200V and a blocked force at 1200V of 0.102N was observed, as shown in FIG. 23. The blocked force measurement is ([0.102 N]/[0.1363 N])=74% of the model prediction.

FIG. 24 is a graphical illustration 320 depicting blocked force versus axial displacement demonstrating the difference between the solid dielectric elastomer transducer roll in compression versus tension in accordance with one embodiment of the present invention. Measuring blocked force on the INSTRON instrument, shows a clear difference between using the solid dielectric elastomer transducer roll in compression 322 versus tension 324, consistent with the slope differences observed in dC/dx. In compression, layers of the solid dielectric elastomer transducer roll undergo localized buckling rather than uniform compression. This occurs at forces (0.1 N) lower than the Euler buckling limit for the entire column (1.5N calculated, 1.4 N observed).

FIG. 25 is a graphical illustration 326 of blocked force versus longitudinal displacement showing the difference between the solid dielectric elastomer transducer roll in compression 328 versus tension 330 in accordance with one embodiment of the present invention.

FIG. 26 is a graphical representation 332 of stiffness of solid dielectric elastomer transducer rolls in accordance with one embodiment of the present invention. The simplest prediction of stiffness for the solid rolls is to neglect electrode stiffness and the rigid boundary conditions:

k _(simple) =YA/l=[0.6E6 Pa]*([2*160E-3 m]*[40E-6 m])/[14E-3 m]=548.6 N/m.

This estimate of the stiffness is relatively good. Observed stiffness is higher than theoretical by only 6-13% in these two samples.

[582 N/m,621 N/m]·/[548.6 N/m]=[1.06 1.13]

This suggests that the effect of the electrode on the stiffness of the solid dielectric elastomer transducer rolls is relatively small and not the 2× factor in the active area that was considered in the dC/dx calculation above. It appears a better assumption may be to treat the electrode stiffness as negligible and to estimate that the observed dC/dx is about 63% of that expected by the model.

FIG. 27 illustrates a solid dielectric elastomer transducer roll 400 in flat roll mode where the roll 400 is placed under compression 402 in a radial direction rather than in an axial direction in accordance with one embodiment of the present invention. As shown, a portion of the solid dielectric elastomer transducer roll 400 is clamped between jaws 404 a, 404 b such that is compresses the transducer roll 400 radially rather axially. Experimental results indicate that the peak capacitance change dC/dx in radial (“flat roll”) mode is approximately 5-times the capacitance change dC/dx in axial mode.

FIG. 28 illustrates a geometric model 410 of a solid dielectric elastomer transducer roll 412 in radial (“flat roll”) mode where the roll 412 is placed under compression in a radial direction in accordance with one embodiment of the present invention. The cross-sectional area of the uncompressed roll 412 is depicted as a circle in phantom, whereas the cross-sectional area A(x) of the roll 412′ under radial compression is depicted in solid line as a flattened elongated structure with flat regions in the center over a length l and rounded ends. The model assumes the following:

Long out of plane→Plane strain;

Incompressible→A(x)=A₀; and

Flat regions slip→Equal strain around perimeter P.

The geometric model for the solid dielectric elastomer transducer roll 412 in radial mode (“flat roll”) is described by the following equations:

$\begin{matrix} {P_{0} = {\pi \; x_{0}}} & {{Eq}.\mspace{14mu} 57} \\ {{P(x)} = {{2} + {\pi \left( {x_{0} - x} \right)}}} & {{Eq}.\mspace{14mu} 58} \\ {A_{0} = {\frac{\pi}{4}x_{0}^{2}}} & {{Eq}.\mspace{14mu} 59} \\ {{A(x)} = {{\left( {x_{0} - x} \right)} + {\frac{\pi}{4}\left( {x_{0} - x} \right)^{2}}}} & {{Eq}.\mspace{14mu} 60} \\ {A_{0} = {A(x)}} & {{Eq}.\mspace{14mu} 61} \\ {{\frac{\pi}{4}x_{0}^{2}} = {{\left( {x_{0} - x} \right)} + {\frac{\pi}{4}\left( {x_{0} - x} \right)^{2}}}} & {{Eq}.\mspace{14mu} 62} \\ { = \frac{\pi \left( {x_{0}^{2} - \left( {x_{0} - x} \right)^{2}} \right)}{4\left( {x_{0} - x} \right)}} & {{Eq}.\mspace{14mu} 63} \\ {{P(x)} = {{2} + {\pi \left( {x_{0} - x} \right)}}} & {{Eq}.\mspace{14mu} 64} \\ \begin{matrix} {{\lambda_{P}(x)} = \frac{P(x)}{P}} \\ {= \frac{P(x)}{\pi \; x_{0}}} \end{matrix} & {{Eq}.\mspace{14mu} 65} \\ {C = {C_{0}\lambda_{P}^{2}}} & {{Eq}.\mspace{14mu} 66} \end{matrix}$

FIG. 29 is a graphical illustration 414 depicting stretch ratio versus percent compression in a radial direction of a solid dielectric elastomer transducer roll in accordance with one embodiment of the present invention. Stretch ration [L/L₀] is shown along the vertical axis and percent compression [x/x₀] is shown along the horizontal axis. The curve 416 shows non-linear behavior of stretch ration versus percent compression.

FIG. 30 illustrates a static equilibrium diagram 418 of a solid dielectric elastomer transducer roll 420 in radial compression (“flat roll”) mode under static load in accordance with one embodiment of the present invention. Static equilibrium is defined as follows:

F _(elec) +F _(S) +F _(L)=0  Eq. 67

where F_(elec) is electric force, F_(S) is spring force and F_(L) is an external load. The electric force is proportional to the capacitance change dC/dx which is in turn proportional to the stretch ratio of the dielectric layers λ=P/P₀. Because this stretch is approximately quadratic with respect to compression of the roll, (FIGS. 29 and 31), the electric force, which is the slope of the capacitance curve, can be approximated with a single constant such that dC/dx=k₁x. The spring force is also approximated well with a single term such that F_(s)=k₃x²

½V ²(k ₁ x)+k ₃ x ² +F _(L)=0  Eq. 68

k ₁ V ²/2 x+k ₃ x ² +F _(L)=0  Eq. 69

k ₃ x ²+(½k ₁ V ²)x+F _(L)=0  Eq. 70

The equilibrium displacement of the roll subjected to the static load is found from the roots of the quadratic equation, where a=k₃, b=½ k₁V² and c=F_(L).

x=[−b±√(b ²−4ac)]/2a  Eq. 71

The Pseudo-DC Roll Model

F _(elec)=½V ² dC/dx  Eq. 72

F _(elec)=½V ²(k ₁ x)  Eq. 73

F _(S) =k ₃ x ²  Eq. 74

F _(L)=−4,[N],for example.

FIG. 31 is a graphical illustration 422 depicting capacitance versus compression in a radial direction of a solid dielectric elastomer transducer roll in flat roll mode in accordance with one embodiment of the present invention. Capacitance C[F] is shown along the vertical axis and compression x[m] is shown along the horizontal axis. The flat roll model curve 424 provides a reasonable first approximation of the capacitance change versus compression as compared to the measurements results 426. Potential contributors to the difference between actual measurements 426 and the model 424 may be that just 7.5 mm of 10 mm active length was compressed in an INSTRON test instrument and the rigid boundary may limit extension of the outer layers.

FIGS. 32A, 32B, 32C and 32D illustrate a solid dielectric elastomer transducer roll 430 under increasing compression force in a radial direction in accordance with one embodiment of the present invention. From left to right, the solid dielectric elastomer transducer roll 430 undergoes increasing compression force such that the roll 430 in under no compression force, roll 430′ is under greater compression force than the roll 430, roll 430″ is under greater compression force than the roll 430′, and the roll 430′″ is under greater compression force than the roll 430″. As shown in FIGS. 32B, 32C and 32D, the roll begins to delaminate as it is subjected to increasing greater compression forces. This delamination causes deviation from the model, and presents a practical limit on compression of the roll.

FIG. 33 illustrates a finite element analysis model 432 of a solid dielectric elastomer transducer roll 434 undergoing radial compression in accordance with one embodiment of the present invention and indicates where stretch orientation is and is not well-aligned with the orientation of the layers.

FIG. 34 illustrates the delamination of inner layers 434 of a solid dielectric elastomer transducer roll 436 undergoing radial compression in accordance with one embodiment of the present invention. As the finite element analysis predicts, delamination occurs in regions where the principal stretch is oriented through the thickness of dielectric films.

As for other details of the present invention, materials and alternate related configurations may be employed as within the level of those with skill in the relevant art. The same may hold true with respect to process-based aspects of the invention in terms of additional acts as commonly or logically employed. In addition, though the invention has been described in reference to several examples, optionally incorporating various features, the invention is not to be limited to that which is described or indicated as contemplated with respect to each variation of the invention. Various changes may be made to the invention described and equivalents (whether recited herein or not included for the sake of some brevity) may be substituted without departing from the true spirit and scope of the invention. Any number of the individual parts or subassemblies shown may be integrated in their design. Such changes or others may be undertaken or guided by the principles of design for assembly.

Various aspects of the subject matter described herein are set out in the following numbered clauses in any combination thereof:

1. A method for making a rolled dielectric elastomer transducer, comprising: applying an electrode material on a first side and a second side of a first dielectric film; laminating the first dielectric film onto a side of a second dielectric film to produce a dielectric film laminate; and rolling the dielectric film laminate into a solid dielectric elastomer transducer roll.

2. The method according to claim 1, wherein applying the electrode material comprises applying at least a first layer of electrode material on the first side of the first dielectric film; and applying at least a second layer of the electrode material on the second side of the first dielectric film; and wherein the at least first layer and the at least second layer of the electrode material are offset relative to each other.

3. The method according to claim 2, further comprising applying at least one additional first layer of electrode material juxtaposed and spaced apart from the at least one first layer of the electrode material on the first side of the first dielectric film, wherein the at least one additional first layer of electrode material on the first side of the first dielectric film partially overlaps the at least one second layer of the electrode material on the second side of the first dielectric film.

4. The method according to claim 3, further comprising segmenting the solid dielectric elastomer transducer roll into two or more individual solid dielectric elastomer transducer rolls at the region where the at least one additional first layer on the first side of the first pre-strained dielectric film overlaps with the at least one second layer of the electrode material on the second side of the first pre-strained dielectric film.

5. The method according to any one of claims 1 to 4, further comprising pre-straining the first and second dielectric films.

6. The method according to any one of claims 1 to 5, further comprising applying an electrically conductive adhesive on a first end and a second end of the solid dielectric elastomer transducer roll; and applying an electrical terminal on the first and second ends of the solid dielectric elastomer transducer roll.

7. The method according to claim 6, further comprising applying a solvent on the first and second ends of the solid dielectric elastomer transducer roll prior to applying the electrically conductive adhesive.

8. An apparatus, comprising a drive mechanism for receiving a carrier plate having a dielectric film laminate located on a first surface thereof, the drive mechanism configured to drive the carrier plate in a first direction; and a scrub roller configured to counter-rotate in a second direction relative to the first direction, the scrub roller configured to frictionally engage the dielectric film to wind the dielectric film laminate into a solid dielectric elastomer transducer roll.

9. The apparatus according to claim 8, further comprising a motion control system for controlling the velocity of the drive mechanism and the scrub roller.

10. The apparatus according to claim 9, wherein the motion control system is configured to control the velocity of the carrier plate V_(plate) in the first direction and the velocity of the scrub roller V_(scrub) in the second opposite direction such that |V_(plate)|=|V_(scrub)|.

11. The apparatus according to claim 9, wherein the motion control system is configured to control the velocity of the carrier plate V_(plate) in the first direction and the velocity of the scrub roller V_(scrub) in the second opposite direction and to compensate for the velocity of the solid dielectric elastomer transducer roll such that |V_(plate)|−V_(roll, x)|=|V_(scrub)|.

12. The apparatus according to claim 9, wherein the motion control system is configured to control the velocity of the carrier plate V_(plate) in the first direction and the velocity of the scrub roller V_(scrub) in the second opposite direction and to compensate for the velocity of the solid dielectric elastomer transducer roll and to compensate for dielectric film stretch defined by a stretch coefficient “k” caused by peel stress such that |V_(plate)|−V_(roll, x)|=k|V_(scrub)|.

13. The apparatus according to claim 9, further comprising at least one sensor to sense force and provide a closed loop feedback mechanism to the motion control system.

14. The apparatus according to any one of claims 9 to 13, further comprising a covering positioned over an outside surface of the scrub roller.

15. The apparatus according to claim 14, wherein the covering is made of a non-stick material.

Also, it is contemplated that any optional feature of the inventive variations described may be set forth and claimed independently, or in combination with any one or more of the features described herein. Reference to a singular item, includes the possibility that there are plural of the same items present. More specifically, as used herein and in the appended claims, the singular forms “a,” “an,” “said,” and “the” include plural referents unless the specifically stated otherwise. In other words, use of the articles allow for “at least one” of the subject item in the description above as well as the claims below. It is further noted that the claims may be drafted to exclude any optional element. As such, this statement is intended to serve as antecedent basis for use of such exclusive terminology as “solely,” “only” and the like in connection with the recitation of claim elements, or use of a “negative” limitation. Without the use of such exclusive terminology, the term “comprising” in the claims shall allow for the inclusion of any additional element—irrespective of whether a given number of elements are enumerated in the claim, or the addition of a feature could be regarded as transforming the nature of an element set forth in the claims. Stated otherwise, unless specifically defined herein, all technical and scientific terms used herein are to be given as broad a commonly understood meaning as possible while maintaining claim validity. 

1. A method for making a rolled dielectric elastomer transducer, comprising: applying an electrode material on a first side and a second side of a first dielectric film; laminating the first dielectric film onto a side of a second dielectric film to produce a dielectric film laminate; and rolling the dielectric film laminate into a solid dielectric elastomer transducer roll.
 2. The method according to claim 1, wherein applying the electrode material comprises, applying at least a first layer of electrode material on the first side of the first dielectric film; and applying at least a second layer of the electrode material on the second side of the first dielectric film; and wherein the at least first layer and the at least second layer of the electrode material are offset relative to each other.
 3. The method according to claim 2, further comprising applying at least one additional first layer of electrode material juxtaposed and spaced apart from the at least one first layer of the electrode material on the first side of the first dielectric film, wherein the at least one additional first layer of electrode material on the first side of the first dielectric film partially overlaps the at least one second layer of the electrode material on the second side of the first dielectric film.
 4. The method according to claim 3, further comprising segmenting the solid dielectric elastomer transducer roll into two or more individual solid dielectric elastomer transducer rolls at the region where the at least one additional first layer on the first side of the first pre-strained dielectric film overlaps with the at least one second layer of the electrode material on the second side of the first pre-strained dielectric film.
 5. The method according to claim 1, further comprising pre-straining the first and second dielectric films.
 6. The method according to claim 1, further comprising: applying an electrically conductive adhesive on a first end and a second end of the solid dielectric elastomer transducer roll; and applying an electrical terminal on the first and second ends of the solid dielectric elastomer transducer roll.
 7. The method according to claim 6, further comprising applying a solvent on the first and second ends of the solid dielectric elastomer transducer roll prior to applying the electrically conductive adhesive.
 8. An apparatus, comprising: a drive mechanism for receiving a carrier plate having a dielectric film laminate located on a first surface thereof, the drive mechanism configured to drive the carrier plate in a first direction; and a scrub roller configured to counter-rotate in a second direction relative to the first direction, the scrub roller configured to frictionally engage the dielectric film to wind the dielectric film laminate into a solid dielectric elastomer transducer roll.
 9. The apparatus according to claim 8, further comprising a motion control system for controlling the velocity of the drive mechanism and the scrub roller.
 10. The apparatus according to claim 9, wherein the motion control system is configured to control the velocity of the carrier plate Vplate in the first direction and the velocity of the scrub roller Vscrub in the second opposite direction such that |Vplate|=|Vscrub|.
 11. The apparatus according to claim 9, wherein the motion control system is configured to control the velocity of the carrier plate Vplate in the first direction and the velocity of the scrub roller Vscrub in the second opposite direction and to compensate for the velocity of the solid dielectric elastomer transducer roll such that |Vplate|−|Vroll, x|=|Vscrub|.
 12. The apparatus according to claim 9, wherein the motion control system is configured to control the velocity of the carrier plate Vplate in the first direction and the velocity of the scrub roller Vscrub in the second opposite direction and to compensate for the velocity of the solid dielectric elastomer transducer roll and to compensate for dielectric film stretch defined by a stretch coefficient “k” caused by peel stress such that |Vplate|−|Vroll, x|=k|Vscrub|.
 13. The apparatus according to claim 9, further comprising at least one sensor to sense force and provide a closed loop feedback mechanism to the motion control system.
 14. The apparatus according to claim 9, further comprising a covering positioned over an outside surface of the scrub roller.
 15. The apparatus according to claim 14, wherein the covering is made of a non-stick material. 